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18新利迎百年校庆系列报告(二十六):Asymptotic behavior of the principal eigenvalue of a linear elliptic operator with small/large diffusion
发布单位:18新利        浏览次数:10        发布时间:2020年08月11日

 


报告时间:2020815日(周六)15:00 -- 16:00

报告地点:主楼203

报告题目:Asymptotic behavior of the principal eigenvalue of a linear elliptic operator with small/large diffusion

报告摘要: We shall report our recent progress on a principal eigenvalue problem of a linear second order elliptic operator with small/large diffusion. More specifically, we are concerned with the following eigenvalue problem: -D?φ -2α?m(x)?φ + V (x)φ = λφ in ?, complemented by a general boundary condition including Dirichlet boundary condition and Robin boundary condition: ?φ/?n + β(x)φ = 0 on ??, where β C(??) allows to be positive, sign-changing or negative, and n(x) is the unit exterior normal to ?? at x. The domain ?? R^N  is bounded and smooth, the constants D > 0 and α > 0 are, respectively, the diffusive and advection coefficients, and m C^2(?) , V C(?) are given functions. We aim to determine the asymptotic behavior of the principal eigenvalue of the above eigenvalue problem as the diffusive coefficient D → 0 or D → ∞. Our results, together with those by others where the Nuemann boundary case (i.e., β = 0 on ??) and Dirichlet boundary case were studied, reveal the important effect of advection and boundary conditions on the asymptotic behavior of the principal eigenvalue. The talk is based on a joint work with Guanghui Zhang and Maolin Zhou.

 

报告人简介:彭锐,教授,博士生导师,江苏省特聘教授,入选教育部新世纪优秀人才支持计划 获得江苏省杰出青年基金江苏省数学成就奖,入选江苏省“333人才工程中青年学科带头人。本科毕业于三峡大学,硕士毕业于东南大学,博士毕业于东南大学和澳大利亚新英格兰大学,曾在加拿大纽芬兰大学(AARMS资助)和美国明尼苏达大学IMA(美国NSF资助)从事博士后工作德国洪堡学者获得者。彭锐教授目前的主要研究兴趣包括偏微分方程、动力系统理论以及在生物学、传染病学和化学反应等领域的应用。已在Transactions of the American Mathematical SocietyJournal of Functional AnalysisSIAM Journal on Mathematical AnalysisIndiana University Mathematics JournalJournal of Nonlinear ScienceCalculus of Variations and Partial Differential EquationsSIAM Journal on Applied MathematicsJournal of Mathematical BiologyPhysica DNonlinearityEuropean Journal of Applied MathematicsJournal of Differential Equations等数学杂志发表学术论文多篇。

 





编辑:哈工大(威海)18新利